What is the equation of a circle centered at the origin with radius 13?A.x3 + y3 = 169B.x3 + y3 = 13C.x2 + y2 = 13D.x2 + y2 = 169SUBMITarrow_backPREVIOUS

Break Down the Problem

1. Identify the Characteristics of the Circle: The circle is centered at the origin (0, 0) and has a radius of 13.
2. Recognize the Standard Form of the Circle's Equation: The general equation for a circle in the Cartesian plane centered at the origin is given by the formula: $x^2 + y^2 = r^2$ where $r$ is the radius.

Relevant Concepts

3. Substituting the Radius: Here, the radius $r = 13$. Thus, we need to compute: $r^2 = 13^2 = 169$

Analysis and Detail

4. Write the Equation: By substituting $r^2$ back into the equation: $x^2 + y^2 = 169$

Verify and Summarize

5. Verification: This equation represents a circle with a radius of 13 centered at the origin. The calculated value $169$ corresponds to $13^2$.

Final Answer

The equation of the circle centered at the origin with radius 13 is: $\boxed{x^2 + y^2 = 169}$ Thus, the correct answer is D. x² + y² = 169.